The standard approach for minimizing (REF ) is to generate a set of paired samples \((\theta _i, x_i) \sim p(\theta , x)\)  and use stochastic gradient descent to obtain a minimizer. However, we have observed superior results with sequential neural posterior estimation (SNPE-C) [1]}. It consists of an \(R\) -step procedure in which \(N\)  paired samples are generated per iteration and used to obtain a sequence of approximations of \(p(\theta |x)\) . SNPE-C's particularity is that the data points generated on a given round \(r\)  are sampled from a posterior approximation obtained on round \(r-1\)  fixed with \(x = x_0\) . This leads to approximations which are targeted to better represent the posterior distribution associated with the observed data point. As a result, the approximation of \(p(\theta |x_0)\)  after \(R\)  rounds is often better than with a single round and \(N \times R\)  simulations.
